Spatial filtering in interferometry

ABSTRACT

Spatial filtering of beams in interferometry systems is used to reduce a displacement of the beams from an optical path corresponding to the path of the beams in an optimally-aligned system. By reducing beam displacement from the optical path, the system reduces the magnitude of beam shears and associated non-cyclic errors in linear and angular displacements measured by the interferometry systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of and claims priority toU.S. application Ser. No. 10/379,103, filed on Mar. 4, 2003, whichclaims priority to Provisional Patent Application No. 60/361,480,entitled “REDUCTION OF NON-CYCLIC ERRORS IN INTERFEROMETRY BY SPATIALFILTERING,” to Henry A. Hill, filed on Mar. 4, 2002.

BACKGROUND

This invention relates to interferometers, e.g., linear and angulardisplacement measuring and dispersion interferometers, that measurelinear and angular displacements of a measurement object such as a maskstage or a wafer stage in a lithography scanner or stepper system, andalso interferometers that monitor wavelength and determine intrinsicproperties of gases.

Displacement measuring interferometers monitor changes in the positionof a measurement object relative to a reference object based on anoptical interference signal. The interferometer generates the opticalinterference signal by overlapping and interfering a measurement beamreflected from the measurement object with a reference beam reflectedfrom the reference object.

In many applications, the measurement and reference beams haveorthogonal polarizations and different frequencies. The differentfrequencies can be produced, for example, by laser Zeeman splitting, byacousto-optical modulation, or internal to the laser using birefringentelements or the like. The orthogonal polarizations allow a polarizingbeam-splitter to direct the measurement and reference beams to themeasurement and reference objects, respectively, and combine thereflected measurement and reference beams to form overlapping exitmeasurement and reference beams. The overlapping exit beams form anoutput beam that subsequently passes through a polarizer. The polarizermixes polarizations of the exit measurement and reference beams to forma mixed beam. Components of the exit measurement and reference beams inthe mixed beam interfere with one another so that the intensity of themixed beam varies with the relative phase of the exit measurement andreference beams.

A detector measures the time-dependent intensity of the mixed beam andgenerates an electrical interference signal proportional to thatintensity. Because the measurement and reference beams have differentfrequencies, the electrical interference signal includes a “heterodyne”signal having a beat frequency equal to the difference between thefrequencies of the exit measurement and reference beams. If the lengthsof the measurement and reference paths are changing relative to oneanother, e.g., by translating a stage that includes the measurementobject, the measured beat frequency includes a Doppler shift equal to2νnp/λ, where ν is the relative speed of the measurement and referenceobjects, λ is the wavelength of the measurement and reference beams, nis the refractive index of the medium through which the light beamstravel, e.g., air or vacuum, and p is the number of passes to thereference and measurement objects. Changes in the phase of the measuredinterference signal correspond to changes in the relative position ofthe measurement object, e.g., a change in phase of 2π correspondssubstantially to a distance change L of λ/(2np). Distance 2L is around-trip distance change or the change in distance to and from a stagethat includes the measurement object. In other words, the phase Φ,ideally, is directly proportional to L, and can be expressed as$\begin{matrix}\begin{matrix}{{\Phi = {2\quad p\quad k\quad L}},} \\{{{where}\quad k} = {\frac{2\quad\pi\quad n}{\lambda}.}}\end{matrix} & (1)\end{matrix}$

Unfortunately, the observable interference phase, {tilde over (Φ)}, isnot always identically equal to phase Φ. Many interferometers include,for example, non-linearities such as those known as “cyclic errors.” Thecyclic errors can be expressed as contributions to the observable phaseand/or the intensity of the measured interference signal and have asinusoidal dependence on the change in for example optical path length2pnL. In particular, a first order cyclic error in phase has for theexample a sinusoidal dependence on (4πpnL)/λ and a second order cyclicerror in phase has for the example a sinusoidal dependence on2(4πpnL)/λ. Higher order cyclic errors can also be present as well assub-harmonic cyclic errors and cyclic errors that have a sinusoidaldependence of other phase parameters of an interferometer systemcomprising detectors and signal processing electronics. Differenttechniques for quantifying such cyclic errors are described in commonlyowned U.S. Pat. Nos. 6,137,574, 6,252,688, and 6,246,481 by Henry A.Hill.

There are in addition to the cyclic errors, non-cyclic non-linearitiesor non-cyclic errors. One example of a source of a non-cyclic error isthe diffraction of optical beams in the measurement paths of aninterferometer. Non-cyclic error due to diffraction has been determinedfor example by analysis of the behavior of a system such as found in thework of J.-P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A.Szöke, F. Zemike, P. H. Lee, and A. Javan, “Accurate Laser WavelengthMeasurement With A Precision Two-Beam Scanning MichelsonInterferometer,” Applied Optics, 20(5), 736-757, 1981.

A second source of non-cyclic errors is the effect of “beam shearing” ofoptical beams across interferometer elements and the lateral shearing ofreference and measurement beams one with respect to the other. Beamshears can be caused, for example, by a change in direction ofpropagation of the input beam to an interferometer or a change inorientation of the object mirror in a double pass plane mirrorinterferometer such as a differential plane mirror interferometer (DPMI)or a high stability plane mirror interferometer (HSPMI).

Accordingly, due to errors such as the aforementioned cyclic andnon-cyclic errors, the observable interference phase typically includescontributions in addition to Φ. Thus, the observable phase is moreaccurately expressed as{tilde over (Φ)}=Φ+ψ+ζ,  (2)where ψ and ζ are the contributions due to the cyclic and non-cyclicerrors, respectively.

In displacement measuring applications, the observable phase is oftenassumed equal to 2pkL, which allows one to readily determine L from themeasured phase. In many cases, this is a reasonable approximation,particularly where the contribution to due cyclic and/or non-cyclicerrors are small, or the level of accuracy required by the applicationis relatively low. However, in applications demanding a high level ofprecision, cyclic and/or non-cyclic errors should be accounted for. Forexample, high precision displacement measurement requirements ofintegrated circuit micro-lithography fabrication have become verydemanding, in part because of the small field limitations of imagingsystems in steppers and scanners and in part because of the continuingreduction in the size of trace widths on wafers. The requirement of highprecision displacement measurement with steppers and scanners istypically served with plane mirror interferometers with one of theexternal mirrors of the plane mirror interferometers attached to a stagemirror of the stepper or scanner. Because the wafer is typically notflat, the orientation of the wafer stage of a stepper or scanner mustalso be adjusted in one or more angular degrees of freedom to compensatefor the non-flatness of the wafer at exposure sites on a wafer. Thecombination of the use of plane mirror interferometers and the change inone or more angular degrees of freedom is a source of lateral shear ofoptical beams across interferometer elements. Effects of beam shears ofa reference beam and a measurement beam may be represented effectivelyas a common mode beam shear and a differential beam shear. Thedifferential beam shear is the difference in lateral shear of referenceand measurement and the common mode beam shear is the average lateralshear of the reference and measurement beams.

The cited source of lateral beam shear presents a potentially seriousproblem in distance measuring interferometry. For a measurement leglength of 1 meter, a typical value for a change in angular orientationof a stage mirror of 0.0005 radians, and a double-pass plane mirrorinterferometer, the relative lateral shear between the reference and themeasurement components of the output beam of the interferometer is 2millimeters. For a relative lateral shear of 2 millimeters, a beamdiameter of 6 millimeters, and wavefront errors in the output beams ofthe order of λ/20, an error will be generated in the inferred distancemeasurement of >/˜1 nanometer. This error is a non-cyclic error and canpose a serious limitation to micro-lithographic applications of steppersand scanners in integrated circuit fabrication.

Wavefront errors are produced by imperfections in transmissive surfacesand imperfections in components, e.g., retroreflectors and phaseretardation plates, and/or coupling into single-mode and multi-modeoptical fibers that produce undesired deformations of wavefronts ofbeams. Non-cyclic errors are also introduced in coupling into differentlongitudinal modes of a multi-mode optical fiber as a result of beamshears at the coupling interface to the multi-mode optical fiber.

In dispersion measuring applications, optical path length measurementsare made at multiple wavelengths, e.g., 532 nanometers and 1064nanometers, and are used to measure dispersion of a gas in themeasurement path of a distance measuring interferometer. The dispersionmeasurement can be used to convert a change in optical path lengthmeasured by the distance measuring interferometer into a correspondingchange in physical length. Such a conversion can be important sincechanges in the measured optical path length can be caused by gasturbulence and/or by a change in the average density of the gas in themeasurement arm even though the physical distance to the measurementobject is unchanged.

When working to position-measurement accuracy of approximately onenanometer or better and for distance measuring interferometry usingdispersion interferometry to correct for the effects of gas in themeasuring path, the cited non-cyclic errors are amplified by thereciprocal dispersive power of the gas, Γ. For the Nb:YAG laser beamwith a wavelength of 1064 nm and the frequency doubled Nb:YAG laser witha beam wavelength of 532 nanometers, Γ≡75. For the 633 nanometer HeNelaser beam and a second beam at 316 nanometer, Γ≡25. Thus, forhigh-accuracy interferometry (accuracy in the 1 nanometer regime orbetter) it is necessary to reduce the effect of the lateral beam shearinduced non-cyclic errors in the dispersion interferometry byapproximately two orders of magnitude beyond that required for thecorresponding distance measuring interferometry, an accuracy in the 0.01nanometer regime or better.

Both common mode and differential beam shear can further compromise theaccuracy of an interferometer where the interferometer output beam iscoupled into a fiber optic pick-up (FOP) to transport the interferometeroutput beam to a remotely located detector.

SUMMARY

Spatial filtering of beams in interferometry systems is used to reduce adisplacement of the beams from an optical path corresponding to the pathof the beams in an optimally-aligned system (e.g., where the measurementbeam is normally incident on the measurement object). By reducing beamdisplacement from the optimal optical path, the system reduces amagnitude of beam shears and associated non-cyclic errors in linear andangular displacements measured by the interferometry systems. Thespatial filtering can also reduce (e.g., eliminates) generation ofnon-cyclic errors that arise from Fresnel diffraction at, e.g.,boundaries of optical elements. Interferometry systems implementing suchspatial filtering can be advantageously incorporated intomicrolithography and beam writing applications.

In general, in a first aspect, the invention features a method includingdirecting a first beam and a second beam along respective paths, whereinthe first beam contacts a measurement object and changes in theorientation of the measurement object cause a displacement of the firstbeam from a nominal beam path, and wherein the first and second beamsare derived from a common source, spatial filtering the first beam afterit contacts the measurement object, wherein the spatial filteringreduces the displacement of the first beam from the optical path, andcombining the first and second beams to form an output beam, wherein theoutput beam includes information about an optical path length differencebetween the first and second beams.

Embodiments of the method can include one or more of the followingfeatures and/or features of other aspects.

Displacement of the first beam from the nominal beam path can cause ameasurable interferometric phase derived from the output beam to deviatefrom the expression Φ=pknL, where p is an integer, k is the wavenumberof the output beam, and nL corresponds to the optical path lengthdifference. The deviation can include a non-cyclic error term thatvaries in a nonperiodic way on the optical path length difference.

The nominal path can correspond to the first beam path when themeasurement object is in a reference oriented. In some embodiments, themeasurement beam is normally incident on the measurement object when themeasurement object is in the reference orientation.

The first beam can be spatial filtered prior to or after being combinedwith the second beam.

In general, in another aspect, the invention features a method includingdirecting a first beam and a second beam along respective paths, whereinthe first beam contacts a measurement object (e.g., a plane mirror) andwherein the first and second beams are derived from a common source,spatial filtering the first beam after it contacts the measurementobject, and combining the first and second beams to form an output beam,wherein the output beam includes information about an optical pathlength difference between the first and second beams.

Embodiments of the method can include one or more of the followingfeatures and/or features of other aspects. Changes in the orientation ofthe measurement object can cause a displacement of the first beam from anominal beam path. The spatial filtering can reduce the displacement ofthe first beam from the nominal beam path. The nominal path cancorrespond to the first beam path when the measurement object is in areference oriented. In some embodiments, the first beam can be normallyincident on the measurement object when the measurement object is in thereference orientation.

The displacement of the first beam from the nominal beam path can causea measurable interferometric phase derived from the output beam todeviate from the expression Φ=pknL, where p is an integer, k is thewavenumber of the output beam, and nL corresponds to the optical pathlength difference. The deviation can include a non-cyclic error termthat varies in a nonperiodic way on the optical path length difference.

The first and second beams can be directed along separate paths by aninterferometer (e.g., a high stability plane mirror interferometer). Thefirst beam can contact the measurement object more than once (e.g.,twice).

Spatial filtering can include focusing the first beam onto a pinholeaperture. The focused beam exiting the pinhole aperture can becollimated.

The method can also include detecting the measurable interference phaseand determining information related to the optical path lengthdifference based on the detected phase. Spatial filtering can reducedeviations of the phase from the expression Φ=pknL. In some embodiments,spatial filtering reduces the contribution of a non-linear non-cyclicerror term to the measurable phase.

The first beam is spatial filtered prior to or after being combined withthe second beam.

In general, in a further aspect, the invention features a methodincluding directing a first beam and a second beam along respectivepaths, wherein the first and second beams are derived from a commonsource, combining the first and second beams to form an output beam,wherein the output beam comprises information about an optical pathlength difference between the first and second beams, and spatialfiltering the first beam, wherein the spatial filtering reducesdeviations of a measurable interferometric phase derived from the outputbeam from the expression Φ=pknL, where p is an integer, k is thewavenumber of the output beam, and nL corresponds to the optical pathlength difference.

Embodiments of the method can include one or more features of otheraspects.

In general, in a further aspect, the invention features an apparatus,including an interferometer which during operation directs a first beamand a second beam along respective paths and then combines the first andsecond beams to produce an output beam, wherein the first beam contactsa measurement object and changes in the orientation of the measurementobject cause a displacement of the first beam from a nominal beam path,and wherein the output beam comprises information about an optical pathlength difference between the first and second beams. The interferometrysystem also includes a spatial filter positioned in the path of thefirst beam, wherein the spatial filtering reduces the displacement ofthe first beam from the nominal beam path.

Embodiments of the apparatus can include one or more of the followingfeatures and/or features of other aspects.

The apparatus can include a detector positioned to detect an intensityof the output beam. Additionally, the apparatus can include anelectronic controller coupled to the detector, which during operationmonitors an interference phase related to the optical path lengthdifference between the first and second beams.

The displacement of the first beam from the nominal beam path can causea measurable interferometric phase derived from the output beam todeviate from the expression Φ=pknL, where p is an integer, k is thewavenumber of the output beam, and nL corresponds to the optical pathlength difference. The deviation can include a non-cyclic error termthat varies in a nonperiodic way on the optical path length difference.

The interferometer can direct the first beam to contact the measurementobject more than once (e.g., twice). In some embodiments, theinterferometer is a high stability plane mirror interferometer.

The spatial filter can include a focusing lens and a pinhole aperture,and during operation the focusing lens focuses the first beam onto thepinhole aperture. The spatial filter can further include a collimatinglens, which during operation collimates the focused beam exiting thepinhole aperture.

The nominal path can correspond to the path of the first beam when themeasurement object is in a reference orientation. In some embodiments,the first beam is normally incident on the measurement object when themeasurement object is in the reference orientation.

The spatial filter can be positioned in the path of the output beam.

The apparatus can include a light source which during operationgenerates an input beam from which the interferometer derives the firstand second beams.

In a further aspect, the invention features a lithography system for usein fabricating integrated circuits on a wafer. The system includes astage for supporting the wafer, an illumination system for imagingspatially patterned radiation onto the wafer, a positioning system foradjusting the position of the stage relative to the imaged radiation,and the foregoing apparatus for monitoring the position of the waferrelative to the imaged radiation.

In another aspect, the invention features a lithography system for usein fabricating integrated circuits on a wafer. The system includes astage for supporting the wafer, and an illumination system including aradiation source, a mask, a positioning system, a lens assembly, and theforegoing apparatus, wherein during operation the source directsradiation through the mask to produce spatially patterned radiation, thepositioning system adjusts the position of the mask relative to theradiation from the source, the lens assembly images the spatiallypatterned radiation onto the wafer, and the apparatus monitors theposition of the mask relative to the radiation from the source.

In another aspect, the invention features a beam writing system for usein fabricating a lithography mask. The system includes a sourceproviding a write beam to pattern a substrate, a stage supporting thesubstrate, a beam directing assembly for delivering the write beam tothe substrate, a positioning system for positioning the stage and beamdirecting assembly relative one another, and the foregoing apparatus formonitoring the position of the stage relative to the beam directingassembly.

In general, in a further aspect, the invention features a method formonitoring the position of a measurement object, including directing afirst beam and a second beam along respective paths, wherein the firstbeam contacts the measurement object and wherein the first and secondbeams are derived from a common source, spatial filtering the first beamafter it contacts the measurement object, combining the first and secondbeams to form an output beam either before or after spatial filteringthe first beam, detecting a phase of the output beam related to anoptical path length difference between the first and second beams, andmonitoring the position of the measurement object based on the detectedphase.

Embodiments of the method can include one or more of the features ofother aspects.

In a further aspect, the invention features a lithography method for usein fabricating integrated circuits on a wafer that includes supportingthe wafer on a moveable stage, imaging spatially patterned radiationonto the wafer, adjusting the position of the stage, and monitoring theposition of the stage using the foregoing method.

In another aspect, the invention features a lithography method for usein the fabrication of integrated circuits including directing inputradiation through a mask to produce spatially patterned radiation,positioning the mask relative to the input radiation, monitoring theposition of the mask relative to the input radiation using the foregoingmethod, and imaging the spatially patterned radiation onto a wafer.

In yet a further aspect, the invention features a lithography method forfabricating integrated circuits on a wafer including positioning a firstcomponent of a lithography system relative to a second component of alithography system to expose the wafer to spatially patterned radiation,and monitoring the position of the first component relative to thesecond component using the foregoing method.

In another aspect, the invention features a method for fabricatingintegrated circuits including the foregoing lithography method(s) and/orusing the foregoing lithography system(s).

In another aspect, the invention features a method for fabricating alithography mask including directing a write beam to a substrate topattern the substrate, positioning the substrate relative to the writebeam, and monitoring the position of the substrate relative to the writebeam using the foregoing method.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. In case of conflict withpublications, patent applications, patents, and other referencesmentioned incorporated herein by reference, the present specification,including definitions, will control.

Other features, objects, and advantages of the invention will beapparent from the following detailed description.

DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of an interferometry system including aspatial filter.

FIG. 2(a) is a schematic diagram of a spatial filter.

FIG. 2(b) and FIG. 2(c) are diagrams illustrating a beam profile beforeand after spatial filtering, respectively.

FIG. 3 is a schematic diagram of another interferometry system includinga spatial filter.

FIG. 4 is a schematic diagram of the interferometry system shown in FIG.3 with the spatial filter in a different position.

FIG. 5(a) is a schematic diagram of a further interferometry systemincluding a spatial filter.

FIG. 5(b)-5(d) are schematic diagrams of afocal systems.

FIG. 6 is a schematic diagram of a lithography system that includesinterferometry system and is used to make integrated circuits.

FIG. 7 and FIG. 8 are flow charts that describe steps for makingintegrated circuits.

FIG. 9 is a schematic diagram of a beam writing system that includes aninterferometry system.

DETAILED DESCRIPTION

Referring to FIG. 1, an interferometry system 100 includes ahigh-stability plane mirror interferometer (HSPMI) indicated by numeral10 and plane mirror measurement object 60. Interferometer 10 includes apolarizing beam splitter 20, a reference mirror 28, a retroreflector 30,and a pair of quarter wave plates 22 and 24.

During operation of interferometry system 100, a source 12 directs aninput beam 14 to interferometer 10. Input beam 14 includes twoorthogonally polarized components that have different frequencies. Thetwo frequency components of input beam 14 can be generated in source 12by can be produced, for example, by laser Zeeman splitting, byacousto-optical modulation, or internal to the laser using birefringentelements or the like. Prior to contacting interferometer 10, input beam14 is incident on polarization beam-splitter 38, which transmits ameasurement component of input beam 14 and reflects a second component.The first and second components are referred to as the measurment andreference beams, respectively. The reference and measurement beams arepolarized orthogonal and parallel to the plane of FIG. 1, respectively.A mirror 36 directs the reference beam along a path parallel to themeasurement beam towards interferometer 10.

Within interferometer 10, the reference beam contacts a secondpolarizing beam splitter 20, which directs the reference beam to reflectfrom a reference mirror 28. Prior to and after reflecting from referencemirror 28, the reference beam passes through a quarter wave plate 22.Quarter wave plate 22 retards the reference beam's polarization so thatthe reflected reference beam is transmitted by polarizing beam splitter20. A retroreflector directs the once-reflected reference beam backtowards quarter wave plate 22 and reference mirror 28, which reflectsthe reference beam back towards polarizing beam splitter 20. Thereference beam's double pass through quarter wave plate 22 transformsits polarization so that it is reflected by polarizing beam splitter 20,exiting interferometer 10 as output reference beam 18.

The measurement beam is initially transmitted by polarizing beamsplitter 20 to reflect from measurement object 60, passing through aquarter wave plate 24 both before and after reflection resulting in thebeam's polarization being rotated by 90°. The reflected measurement beamcontacts polarizing beam splitter 20, which now reflects the measurementbeam toward retroreflector 30. Retroreflector 30 directs the measurementbeam back towards polarizing beam splitter 20, which reflects the beamtowards measurement object 60. Reflecting from measurement object 60 andpassing through quarter wave plate 24 twice results in another 90°rotation of the measurement beam polarization. Accordingly, polarizingbeam splitter 20 now transmits the measurement beam, which exitsinterferometer 10 as output measurement beam 16.

Variations in the orientation of measurement object 60 cause adisplacement of output measurement beam 16 from a nominal measurementbeam path. The nominal measurement beam path is defined as the path themeasurement beam traverses when it is normally incidence on measurementobject 60.

A mirror 34 and a polarizing beam splitter 32 combine output beams 16and 18 into a single, substantially coextensive output beam 20.Interferometer 10 introduces a phase Φ₁ between the reference andmeasurement beams of output beam 20. Phase Φ₁ includes effects of alinear displacement of plane mirror 60, cyclic errors, and non-cyclicerrors. Phase Φ₁ is measured as the phase of electrical interferencesignal 42 by electronic processor 80 and computer 82. Phase Φ₁ includesthe cyclic errors and non-cyclic errors according to the formula$\begin{matrix}{\Phi_{1} = {{4\quad{k\left\lbrack {{n_{1}L_{1}\quad\cos^{2}\beta_{1}} + {a_{1}n_{10}\quad{\sin^{2}\left( \frac{\beta_{1}}{n_{10}} \right)}}} \right\rbrack}} + \psi_{1} + \zeta_{1}}} & (3)\end{matrix}$where 2L₁ is the relative round trip physical length of the measurementand reference beam paths between interferometer 10 and measurementobject 60, a₁, is the physical distance between the apex ofretroreflector 30 and the center of polarizing beam splitter 20,wavenumber k=2π/λ for wavelength λ of beam 14, n₁ is the index ofrefraction of a medium in the measurement path, n₁₀ is the index ofrefraction of the optical elements of interferometer 10, β₁ is themagnitude of an angular change in orientation of plane mirror 60 from anull position, ψ₁ is function representing the cyclic errors, and ζ₁ isa function representing the non-cyclic errors.

In order to reduce the magnitude of non-cyclic error function ζ₁,measurement beam 16 is directed through a spatial filter 50 located inthe measurement beam path between polarizing beam splitters 20 and 32.Referring to FIG. 2(a), spatial filter 50 includes a focusing lens 52(e.g., a single or compound lens), a stop 55 providing a pinholeaperture 54, and a collimating lens 56 (e.g., a single or compoundlens). Lens 52 focuses measurement beam 16 to pinhole aperture 54. Lens54 collimates the focused beam exiting pinhole aperture 54. Spatialfilter 50 has an axis 58, corresponding to the optical axis of lens 52.The center of pinhole 54 and the optical axis of lens 56 are coincidentwith axis 58. Typically, spatial filter 50 also includes one or morealignment components (e.g., x-y-z stages) for accurately positioning thelenses with respect to the pinhole aperture and the spatial filterrelative to the interferometer. Imperfections (e.g., spatial noiseincluding rays not substantially parallel to axis 58) non-paraxial raysor wavefront variations due to Fresnel diffraction of the measurementbeam from an optical component edge) in output measurement beam 16 aredefocused in an annulus about axis 58. The pinhole blocks most of thisnoise. Accordingly, the-collimated beam exiting the spatial filter issubstantially free of these imperfections.

In some embodiments, the diameter of pinhole aperture 54 is selectedbased on the diameter, D, and wavelength, λ, of the measurement beam,and the focal length of focusing lens 52, ƒ. Focusing lens 52 focusesthe measurement beam to a spot diameter given by$\frac{1.27 \cdot \lambda \cdot f}{D}.$The diameter of pinhole aperture 54 can be selected based on the spotdiameter. For example, the pinhole aperture diameter can be chosen to beequal to or greater than the beam spot diameter (e.g., 1.5 or twice thebeam spot diameter). In some embodiments, the pinhole aperture diameteris approximately on the order of the wavelength of the measurement beam(e.g., 0.5 λ<pinhole aperture diameter<10λ). In embodiments where themeasurement beam diameter is on the order of a few to severalmillimeters (e.g., between about one and 20 millimeters, such as aboutfive millimeters), the pinhole aperture diameter can be between about0.5 and 20 microns (e.g., between about one and 10 microns, such asabout 5 microns).

Spatial filter 50 is oriented relative to interferometer 10 so that axis58 is coincident with the nominal measurement beam path (i.e., the beampath corresponding to the, measurement beam being normally incident onmeasurement object 60. Thus, spatial filter 50 is positioned so thatwhen measurement beam 16 is coincident with axis 58, then themeasurement beam optimally overlaps with reference beam in output beam20. Accordingly, axis 58 corresponds to a measurement beam path forwhich there is no differential beam shear.

In addition to reducing spatial noise in the measurement beam, spatialfilter 50 also reduces a displacement of measurement beam 16 from axis58. This reduction occurs because the transmission properties of spatialfilter 50 vary as a function of a rays distance from the spatialfilter's axis. Typically, transmission is greatest for on-axis rays. Forrays greater than a threshold distance off-axis, transmission can bezero. The effect of reduced off-axis transmission on the measurementbeam is illustrated in FIG. 2(b) and FIG. 2(c). Referring specificallyto FIG. 2(b), a spatial filter has non-zero transmission for rays withina radius γ from axis 58. A measurement beam having a radius δ, anddisplaced from axis 58 by an amount Δ, is incident on the spatialfilter. Referring now to FIG. 2(c), due to the transmission propertiesof the spatial filter, only rays less than γ away from axis 58 aretransmitted. Thus, the spatial filter reshapes the measurement beamprofile, which exits the spatial filter with a radius δ′, and isdisplaced by an amount Δ′ from axis 58, where Δ′<Δ.

In the foregoing example, beam displacement from axis 58 is measuredfrom the geometric center of the beam profile. However, in otherembodiments, other measures of beam displacement can be used, e.g., fromthe axis to the point of highest beam intensity.

The amount by which the spatial filter reduces the beam displacementfrom axis 58 can vary depending on the characteristics of the spatialfilter (e.g., the focal length of lens 52 and/or the pinhole aperturediameter). In some embodiments, the the spatial filter reduces the beamdisplacement from axis 58 by more than about 20 percent (e.g., more than35 percent, such as 50 percent or more).

The transmission properties of spatial filter 50 can be represented by atransmission function T₁ (ξ,η) where ξ and η are orthogonal coordinatesin the plane of spatial filter 50 and parallel and orthogonal to theplane of FIG. 2(a), respectively.

In some embodiments, transmission function T₁ (ξ,η) can be approximatedby a bell shape or Gaussian shape in going from a central region to anedge of spatial filter 50 to reduce or eliminate the generation ofFresnel diffraction that can produce non-cyclic errors in electricalinterference signal 42. Transmission function T₁ (ξ,η) may exhibitsymmetry properties such as azimuthal symmetry about a center,non-symmetric azimuthal properties about a center, an inversionsymmetry, e.g., T₁ (ξ,η)=T₁ (−ξ,−η) or non-symmetric properties onreflection about ξ=0 and/or η=0.

An example is presented wherein the amplitude profile of the outputreference and measurement beams from polarizing beam splitter 20 areGaussian and transmission function T₁ (ξ,η) exhibits inversion symmetry.Transmission function T₁ (ξ,η) is further represented as a function thatis Gaussian in coordinates ξ and η with different width parameters,e.g., $\begin{matrix}{{T_{1}\left( {\xi,\eta} \right)} = {\exp\left\lbrack {{{- 2}\left( {\frac{\xi^{2}}{u_{F}^{2}} + \frac{\eta^{2}}{v_{F}^{2}}} \right)} + {{\mathbb{i}}\quad{\varphi_{1}\left( {\xi,\eta} \right)}}} \right\rbrack}} & (4)\end{matrix}$where u_(F) and ν_(F) are the radii that T₁ (ξ,η)^(1/2) has values of1/e in the (ξ,0) and (0,η) planes, respectively, and φ₁ (ξ,η) is a phaseshift introduced by spatial filter 50. The amplitude profiles A_(1,r)and A_(1,m) of the output reference and measurement beams 18 and 16,respectively, at spatial filter 50 are expressed as $\begin{matrix}{{{A_{1,r}\left( {\xi,\eta} \right)} = {A_{0}\quad{\exp\left\lbrack {{- \left( \frac{\xi}{u_{B}} \right)^{2}} - \left( \frac{\eta}{v_{B}} \right)^{2}} \right\rbrack}}},} & (5) \\{{A_{1,m}\left( {\xi,\eta} \right)} = {A_{0}\quad\exp\left\{ {{- \frac{\left( {\xi - b_{1,\xi}} \right)^{2}}{u_{B}^{2}}} - \frac{\left( {\eta - b_{1,\eta}} \right)^{2}}{v_{B}^{2}}} \right\}}} & (6)\end{matrix}$where u_(B) and ν_(B) are the radii that A_(1,r) (ξ,η)/A₀ and A_(1,m)(ξ,η)/A₀ each have a values of 1/e in the (ξ,0) and (0,η) planes,respectively, and b_(1,ξ) and b_(1,η) are displacements, i.e., beamshears of the output measurement beam 16 with respect to spatial filter50 in the ξ and η coordinates, respectively. The amplitude of thereference and measurement beams have been selected to have the sameamplitudes A₀ so as to illustrate in a simple example features of theinvention without departing from the scope and spirit of the presentinvention.

Beam shears b_(1,ξ) and b_(1,η) for the first embodiment are the beamshears that would be exhibited at detector 40 if spatial filter 50 wereremoved and areb_(1,ξ)=4L₁θ_(1,ξ),  (7)b_(1,η)=4L₁θ_(1,η),  (8)where θ_(1,ξ), and θ_(1,η) are the changes in orientation of planemirror 60 in the plane and orthogonal to the plane, respectively, ofFIG. 1.

The amplitude A_(1,m,T) (ξ,η) of the measurement beam transmitted byspatial filter 50 is given by the product of Equations (4) and (6) as$\begin{matrix}{{A_{1,m,T}\left( {\xi,\eta} \right)} = {T^{1/2}\quad\left( {\xi,\eta} \right)\quad A_{1,m}\quad\left( {\xi,\eta} \right)}} & (9) \\{\quad{= {A_{0}\quad\exp\begin{Bmatrix}\begin{matrix}{{{- \left\lbrack {\xi - {\left( \frac{u_{B,F}^{2}}{u_{B}^{2}} \right)b_{1,\xi}}} \right\rbrack^{2}}\left( \frac{1}{u_{B,F}} \right)^{2}} -} \\{\left( \frac{u_{B,F}}{u_{F}} \right)^{2}\left( \frac{b_{1,\xi}}{u_{B}} \right)^{2}}\end{matrix} \\\begin{matrix}{{{- \left\lbrack {\eta - {\left( \frac{v_{B,F}^{2}}{v_{B}^{2}} \right)b_{1,\eta}}} \right\rbrack^{2}}\left( \frac{1}{v_{B,F}} \right)^{2}} -} \\{{\left( \frac{v_{B,F}}{v_{F}} \right)^{2}\left( \frac{b_{1,\eta}}{v_{B}} \right)^{2}} + {{\mathbb{i}}\frac{\varphi_{1}}{2}}}\end{matrix}\end{Bmatrix}}}} & \quad \\{where} & \quad \\{{\frac{1}{u_{B,F}^{2}} = {\frac{1}{u_{B}^{2}} + \frac{1}{u_{F}^{2}}}},} & (10) \\{{\frac{1}{v_{B,F}^{2}} = {\frac{1}{v_{B}^{2}} + \frac{1}{v_{F}^{2}}}},} & (11)\end{matrix}$and φ₁ is the value of φ₁ for beam shears b_(1,ξ) and b_(1,η).

The output measurement beam of beam 20 exhibits an important property.It is evident from Equation (9) that the beam shears b_(1,ξ,T) andb_(1,η,T) of the measurement beam of beam 20 are reduced relative to thecorresponding beam shears of the measurement beam of beam 16 accordingto the formulae $\begin{matrix}{{b_{1,\xi,T} = {\frac{u_{B,F}^{2}}{u_{B}^{2}}b_{1,\xi}}},} & (12) \\{{b_{1,\eta,T} = {\frac{v_{B,F}^{2}}{v_{B}^{2}}b_{1,\eta}}},} & (13)\end{matrix}$respectively. The reduction of the beam shears of the measurement beamof beam 20 reduces the magnitude of non-cyclic errors that wouldotherwise be present. The net effect of reduction of the magnitude ofnon-cyclic errors will depend on the sensitivity of the non-cyclicerrors to beam shear. For example, a non-cyclic error that isproportional to the cube of the beam shear will be reduced by a factorof 8 for (u_(B,F)/u_(B))²=½.

The amplitude A_(1,H) of electrical interference signal 42 is obtainedby integrating the product of amplitudes A_(1,r) and A_(1,m,T) over ξand η coordinates wherein the amplitudes are given by Equations (5) and(9). The resulting expression for A_(1,H) is $\begin{matrix}{A_{1,H} = {{A_{1,H,0}\left( \frac{\sqrt{2}u_{{2\quad B},F}}{u_{B}} \right)}\left( \frac{\sqrt{2}v_{{2\quad B},F}}{v_{B}} \right) \times}} & (14) \\{\quad{\exp\left\lbrack {{{- \left( \frac{u_{{2\quad B},F}}{u_{B,F}} \right)^{2}}\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - {\left( \frac{v_{{2\quad B},F}}{v_{B,F}} \right)^{2}\left( \frac{b_{\eta}}{v_{B}} \right)^{2}}} \right\rbrack}} & \quad \\{where} & \quad \\{{\frac{1}{u_{{2\quad B},F}^{2}} = {\frac{2}{u_{B}^{2}} + \frac{1}{u_{B,F}^{2}}}},} & (15) \\{{\frac{1}{v_{{2\quad B},F}^{2}} = {\frac{2}{v_{B}^{2}} + \frac{1}{v_{B,F}^{2}}}},} & (16)\end{matrix}$and A_(1,H,0) is the amplitude of the electrical interference signal forthe case u_(F)=v_(F)=∞. The effect of φ₁ on amplitude A_(1,H) has beenset to zero in obtaining Equation (14) to illustrate the effect of thespatial filter on the interferometry system.

The value for the reduction of beam shear of the measurement beam ofbeam 20 and the amplitude ratio A_(1,H)/A_(1,H,0) for the case ofu_(F)=u_(F), v_(F)=∞ using Equations (12), (13), and (14) are$\begin{matrix}{{b_{1,\xi,T} = {\left( \frac{1}{2} \right)\quad b_{1,\xi}}},} & (17) \\{{b_{1,\eta,T} = b_{1,\eta}},} & (18) \\{\left( \frac{A_{1,H}}{A_{1,H,0}} \right) = {\left( \frac{2}{3} \right)^{1/2}\quad{{\exp\left\lbrack {{{- \left( \frac{2}{3} \right)}\quad\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - \left( \frac{b_{\eta}}{v_{B}} \right)^{2}} \right\rbrack}.}}} & (19)\end{matrix}$

The values for the reduction of beam shear of the measurement beam ofbeam 20 and the amplitude ratio A_(1,H)/A_(1,H,0) for the case ofu_(B)=u_(F)=v_(B)=v_(F) using Equations (12), (13), and (14) are$\begin{matrix}{{b_{1,\xi,T} = {\left( \frac{1}{2} \right)\quad b_{1,\xi}}},} & (20) \\{{b_{1,\eta,T} = {\left( \frac{1}{2} \right)\quad b_{1,\eta}}},} & (21) \\{\left( \frac{A_{1,H}}{A_{1,H,0}} \right) = {\left( \frac{2}{3} \right)\quad{{\exp\left\lbrack {{{- \left( \frac{2}{3} \right)}\quad\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - {\left( \frac{2}{3} \right)\quad\left( \frac{b_{\eta}}{v_{B}} \right)^{2}}} \right\rbrack}.}}} & (22)\end{matrix}$

The amplitude of electrical interference signal 42 is reduced by theintroduction of spatial filter 50 as shown in Equations (14), (19), and(22). However, the variation of the amplitude of electrical interferencesignal 42 with beam shear is reduced as further evident in Equations(14), (19), and (22). Because of the reduced variation of the amplitude,the amplitude of the electrical interference signal 42 for large beamshears is approximately the same as the amplitude that would be obtainedfor the case of no spatial filtering. A reduction of the variation ofthe amplitude can be beneficial because of a less dynamic range requiredin detector 40 and electronic processor 80 without a degradation ofperformance with respect to signal-to-noise ratio.

Spatial filter 50 can also reduce (e.g., eliminate) generation ofFresnel fringes that would otherwise occur due to a beam being shearedand diffracted at an edge of an optical element. Reduction of theeffects of Fresnel fringes is most effective when spatial filter 50 islocated close to the optical element with the edge, i.e., close in adirection orthogonal to the plane of spatial filter 50. In someembodiments, spatial filter 50 can be located less than about 10centimeters from interferometer 10 (e.g., less than about fivecentimeters, such as about three centimeters or less).

In some embodiments, it may be desirable to place the spatial filter atother locations in the interferometry system. Alternatively, oradditionally, it may be beneficial to place two or more spatial filtersin the interferometry system. Additional spatial filters can increaseeffectiveness in elimination of generation of Fresnel fringes such aswhen there are two or optical elements that have edges that wouldotherwise generate Fresnel fringes.

An example of placing the spatial filter in a different position isshown schematically in FIG. 3, which shows an interferometry system 200having a spatial filter 150 placed in the path of an output beam 116that includes both the reference and measurement beams. System 200includes a HSPMI indicated by numeral 110 with plane mirror measurementobject 160. HSPMI 110 includes reference mirror 128, retroreflector 130,polarizing beam splitter 120, and quarter waveplates 122 and 124. HSPMI110 splits an input beam 114 from a source 112 into a measurementcomponent beam and a reference component beam. HSPMI directs themeasurement component beam to reflect from measurement object 160 twice,and directs the reference component beam to reflect from referencemirror 128 twice before combining the measurement and referencecomponent beams to form output beam 116. A spatial filter 150 is locatedin the path of output beam 116. The output beam exiting spatial filter150 is denoted by numeral 120.

To illustrate the effect of spatial filter 150 on the output beam,assume the spatial filter has a Gaussian transmission function and thatboth the measurement and reference beams in output beam 116 haveGaussian profiles. Amplitudes A_(2,r,T) (ξ,η) and A_(2,m,T) (ξ,η) of thereference and measurement beams, respectively, of transmitted outputbeam 120 are $\begin{matrix}\begin{matrix}{{A_{2,r,T}\left( {\xi,\eta} \right)} = {{T\left( {\xi,\eta} \right)}^{1/2}{A_{r}\left( {\xi,\eta} \right)}}} \\{{= {A_{0}\exp\left\{ {{- \left( \frac{\xi}{u_{B}} \right)^{2}} - \left( \frac{\eta}{v_{B}} \right)^{2} + {i\frac{\varphi_{2,r}}{2}}} \right\}}},}\end{matrix} & (23) \\\begin{matrix}{{A_{2,m,T}\left( {\xi,\eta} \right)} = {{T\left( {\xi,\eta} \right)}^{1/2}{A_{1,m}\left( {\xi,\eta} \right)}}} \\{= {A_{0}\exp}} \\{\begin{Bmatrix}{{{- \left\lbrack {\xi - {\left( \frac{u_{B,F}^{2}}{u_{B}^{2}} \right)b_{2,\xi}}} \right\rbrack^{2}}\left( \frac{1}{u_{B,F}} \right)^{2}} -} \\{{\left( \frac{u_{B,F}}{u_{F}} \right)^{2}\left( \frac{b_{2,\xi}}{u_{B}} \right)^{2}} -} \\{{\left\lbrack {\eta - {\left( \frac{v_{B,F}^{2}}{v_{B}^{2}} \right)b_{2,\eta}}} \right\rbrack^{2}\left( \frac{1}{v_{B,F}} \right)^{2}} -} \\{{\left( \frac{v_{B,F}}{v_{F}} \right)^{2}\left( \frac{b_{2,\eta}}{v_{B}} \right)^{2}} + {i\frac{\varphi_{2,m}}{2}}}\end{Bmatrix},}\end{matrix} & (24)\end{matrix}$where φ_(2,r) and φ_(2,m) are the values of phase shifts introduced byspatial filter 150 for the reference and measurement beams,respectively, of output beam 120.

Beam shears b_(2,ξ) and b_(2,η) for the second embodiment are the beamshears that would be exhibited at detector 140 if spatial filter 150were removed and areb_(2,ξ)=4L₂θ_(2,ξ),  (25)b_(2,η)=4L₂θ_(2,η),  (26)where θ_(2,ξ) and θ_(2,η) are changes in orientation of plane mirror 160in the plane and orthogonal to the plane, respectively, of FIG. 3.

It is evident from Equation (24) that beam shears b_(2,ξ,T) andb_(2,η,T) of output beam 120 are reduced relative to the correspondingbeam shears of components of beam 116 according to the formulae$\begin{matrix}{{b_{2,\xi,T} = {\frac{u_{B,F}^{2}}{u_{B}^{2}}b_{2,\xi}}},} & (27) \\{b_{2,\eta,T} = {\frac{v_{B,F}^{2}}{v_{B}^{2}}{b_{2,\eta}.}}} & (28)\end{matrix}$

The amplitude A_(2,H) of electrical interference signal 142 is obtainedby integrating the product of amplitudes A_(2,r,T) and A_(2,m,T) overthe ξ and η coordinates wherein the amplitudes are given by Equations(23) and (24). The resulting expression for A_(2,H) is $\begin{matrix}{\begin{matrix}{A_{2,H} = {{A_{2,H,0}\left( \frac{\sqrt{2}u_{{2B},{2F}}}{u_{B}} \right)}\left( \frac{\sqrt{2}v_{{2B},{2F}}}{v_{B}} \right) \times}} \\{\exp\left\lbrack {{{- \left( \frac{u_{{2B},{2F}}}{u_{B,{2F}}} \right)^{2}}\left( \frac{b_{2,\xi}}{u_{B}} \right)^{2}} - {\left( \frac{v_{{2B},{2F}}}{v_{B,{2F}}} \right)^{2}\left( \frac{b_{2,\eta}}{v_{B}} \right)^{2}}} \right\rbrack}\end{matrix}{where}} & (29) \\{{\frac{1}{u_{B,{2F}}^{2}} = {\frac{1}{u_{B}^{2}} + \frac{2}{u_{F}^{2}}}},} & (30) \\{{\frac{1}{v_{B,{2F}}^{2}} = {\frac{1}{v_{B}^{2}} + \frac{2}{v_{F}^{2}}}},} & (31) \\{{\frac{1}{u_{{2B},{2F}}^{2}} = {\frac{2}{u_{B}^{2}} + \frac{2}{u_{F}^{2}}}},} & (32) \\{{\frac{1}{v_{{2B},{2F}}^{2}} = {\frac{2}{v_{B}^{2}} + \frac{2}{v_{F}^{2}}}},} & (33)\end{matrix}$and A_(2,H,0) is amplitude electrical interference signal 142 for thecase u_(F)=v_(F)=∞. The effects of φ_(2r) and φ_(2m) on amplitudeA_(2,H) have been set to zero in obtaining Equation (29).

The reduction of beam shear of the measurement beam of beam 120 and theamplitude ratio A_(2,H)/A_(2,H,0) for the case of u_(F)=u_(F), v_(F)=∞using Equations (27), (28), and (29) are $\begin{matrix}{{b_{2,\xi,T} = {\left( \frac{1}{2} \right)b_{2,\xi}}},} & (34) \\{{b_{2,\eta,T} = b_{2,\eta}},} & (35) \\{\left( \frac{A_{2,H}}{A_{2,H,0}} \right) = {\left( \frac{1}{2} \right)^{1/2}{{\exp\left\lbrack {{{- \left( \frac{3}{4} \right)}\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - \left( \frac{b_{\eta}}{v_{B}} \right)^{2}} \right\rbrack}.}}} & (36)\end{matrix}$

The reduction of beam shear of the measurement beam of beam 20 and theamplitude ratio A_(1,H)/A_(1,H,0) for the case ofu_(B)=u_(F)=v_(B)=v_(F) using Equations (27), (28), and (29) are$\begin{matrix}{{b_{2,\xi,T} = {\left( \frac{1}{2} \right)b_{2,\xi}}},} & (37) \\{{b_{2,\eta,T} = {\left( \frac{1}{2} \right)b_{2,\eta}}},} & (38) \\{\left( \frac{A_{2,H}}{A_{2,H,0}} \right) = {\left( \frac{1}{2} \right){{\exp\left\lbrack {{{- \left( \frac{3}{4} \right)}\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - {\left( \frac{3}{4} \right)\left( \frac{b_{\eta}}{v_{B}} \right)^{2}}} \right\rbrack}.}}} & (39)\end{matrix}$

Referring to FIG. 4, in some embodiments, spatial filter 150 canalternatively be placed between HSMPI 110 and measurement object 160.Assuming again, for illustrative purposes, that spatial filter 150 has aGaussian transmission function and the measurement and reference beamshave Gaussian profiles, amplitudes A_(3,r,T) (ξ,η) and A_(3,m,T) (ξ,η)of the reference and measurement beams, respectively, of output beam 120are $\begin{matrix}{{{A_{3,r}\left( {\xi,\eta} \right)} = {A_{0}\exp\left\{ {{- \left( \frac{\xi}{u_{B}} \right)^{2}} - \left( \frac{\eta}{v_{B}} \right)^{2}} \right\}}},} & (40) \\\begin{matrix}{{A_{3,m,T}\left( {\xi,\eta} \right)} = {{T^{1/2}\left( {\xi,\eta} \right)}{A_{3,m}\left( {\xi,\eta} \right)}}} \\{= {A_{0}\exp}} \\{\begin{Bmatrix}{{{- \left\lbrack {\xi - {\left( \frac{1}{2} \right)\left( \frac{u_{B,{2F}}}{u_{{2B},F}} \right)^{2}b_{3,\xi}}} \right\rbrack^{2}}\left( \frac{1}{u_{B,{2F}}} \right)^{2}} -} \\{{\left( \frac{1}{4} \right){\left( \frac{u_{B,F}}{u_{F}} \right)^{2}\left\lbrack {1 + \left( \frac{u_{B}u_{B,{2F}}}{u_{{2B},F}^{2}} \right)^{2}} \right\rbrack}\left( \frac{b_{3,\xi}}{u_{B}} \right)^{2}} -} \\{{\left\lbrack {\eta - {\left( \frac{1}{2} \right)\left( \frac{v_{B,{2F}}}{v_{{2B},F}} \right)^{2}b_{3,\eta}}} \right\rbrack^{2}\left( \frac{1}{v_{B,{2F}}} \right)^{2}} -} \\{{\left( \frac{1}{4} \right){\left( \frac{v_{B,F}}{v_{F}} \right)^{2}\left\lbrack {1 + \left( \frac{v_{B}v_{B,{2F}}}{v_{{2B},F}^{2}} \right)^{2}} \right\rbrack}\left( \frac{b_{3,\eta}}{v_{B}} \right)^{2}} + {i\quad\varphi_{3}^{\prime}}}\end{Bmatrix}.}\end{matrix} & (41)\end{matrix}$where phase φ′₃ is the net effect of the double pass of the measurementbeam through spatial filter 150.

Beam shears b_(3,ξ) and b_(3,η) are the beam shears that would beexhibited at detector 140 if spatial filter 150 were removed and areb_(3,ξ)=4L₃θ_(3,ξ),  (42)b_(3,η)=4L₃θ_(3,η),  (43)where θ_(3,ξ) and θ_(3,η) are changes in orientation of plane mirror 160in the plane and orthogonal to the plane, respectively, of FIG. 4.

It is evident from Equation (41) that beam shears b_(3,ξ,T) andb_(3,η,T) of the measurement beams of output beam 120 are reducedrelative shears b_(3,ξ) and b_(3,η), respectively, according to theformulae $\begin{matrix}{{b_{3,\xi,T} = {\left( \frac{1}{2} \right)\left( \frac{u_{B,{2F}}}{u_{{2B},F}} \right)^{2}b_{3,\xi}}},} & (44) \\{b_{3,\eta,T} = {\left( \frac{1}{2} \right)\left( \frac{v_{B,{2F}}}{v_{{2B},F}} \right)^{2}{b_{3,\eta}.}}} & (45)\end{matrix}$

The amplitude A_(3,H) of electrical interference signal 142 is obtainedby integrating the product of amplitudes A_(3,r) and A_(3,m,T) over theξ and η coordinates wherein the amplitudes are given by Equations (40)and (41). The resulting expression for A_(3,H) is $\begin{matrix}\begin{matrix}{A_{3,H} = {{A_{3,H,0}\left( \frac{\sqrt{2}u_{{2B},{2F}}}{u_{B}} \right)}\left( \frac{\sqrt{2}v_{{2B},{2F}}}{v_{B}} \right) \times \exp}} \\{\begin{Bmatrix}{{{- {\left( \frac{1}{4} \right)\left\lbrack {\left( \frac{u_{B,F}}{u_{F}} \right)^{2} + \left( \frac{u_{B}u_{{2B},{2F}}}{u_{{2B},F}^{2}} \right)^{2}} \right\rbrack}}\left( \frac{b_{3,\xi}}{u_{B}} \right)^{2}} -} \\{{\left( \frac{1}{4} \right)\left\lbrack {\left( \frac{v_{B,F}}{v_{F}} \right)^{2} + \left( \frac{v_{B}v_{{2B},{2F}}}{v_{{2B},F}^{2}} \right)^{2}} \right\rbrack}\left( \frac{b_{3,\eta}}{v_{B}} \right)^{2}}\end{Bmatrix},}\end{matrix} & (46)\end{matrix}$and A_(3,H,0) is amplitude electrical interference signal 242 for thecase u_(F)=v_(F)=∞. The effects of φ′₃ on amplitude A_(3,H) have beenset to zero in obtaining Equation (46) to show in a simple example basicproperties of the invention without departing from the scope and spiritof the invention.

The reduction of beam shear of the measurement beam of beam 120 and theamplitude ratio A_(3,H)/A_(3,H,0) for the case of u_(F)=u_(F), v_(F)=∞using Equations (44), (45), and (46) are $\begin{matrix}{{b_{3,\xi,T} = {\left( \frac{1}{2} \right)b_{3,\xi}}},} & (47) \\{{b_{3,\eta,T} = b_{3,\eta}},} & (48) \\{\left( \frac{A_{3,H}}{A_{3,H,0}} \right) = {\left( \frac{1}{2} \right)^{1/2}{{\exp\left\lbrack {{{- \left( \frac{11}{16} \right)}\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - {\left( \frac{1}{2} \right)\left( \frac{b_{\eta}}{v_{B}} \right)^{2}}} \right\rbrack}.}}} & (49)\end{matrix}$

The reduction of beam shear of the measurement beam of beam 120 and theamplitude ratio A_(3,H)/A_(3,H,0) for the case ofu_(B)=u_(F)=v_(B)=v_(F) using Equations (44), (45), and (46) are$\begin{matrix}{{b_{3,\xi,T} = {\left( \frac{1}{2} \right)b_{3,\xi}}},} & (50) \\{{b_{3,\eta,T} = {\left( \frac{1}{2} \right)b_{3,\eta}}},} & (51) \\{\left( \frac{A_{3,H}}{A_{3,H,0}} \right) = {\left( \frac{1}{2} \right){{\exp\left\lbrack {{{- \left( \frac{11}{16} \right)}\left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - {\left( \frac{11}{16} \right)\left( \frac{b_{\eta}}{v_{B}} \right)^{2}}} \right\rbrack}.}}} & (52)\end{matrix}$

Although the foregoing embodiments all utilize interferometry systemsthat monitor one degree of freedom of a measurement object (e.g.,displacement of the measurement object along one axis), spatial filterscan be employed to reduce the effects of beam shear in systems thatmonitor more than one degree of freedom. For example, spatial filterscan be used in interferometry systems that monitor more than one degreeof freedom of the measurement object. One example of such a system 300is shown in FIG. 5(a). System 300 includes an interferometer indicatedat numeral 310 that measures two degrees of freedom of plane mirrormeasurement object 360, namely the displacement of the measurementobject along an axis parallel to the measurement beams and theorientation of the measurement object about an axis perpendicular to theplane of FIG. 5(a). Interferometer 310 includes a polarizing beamsplitter 320, a reference mirror 328, a retroreflector 330, and quarterwave plates 322 and 324. Additionally, interferometer 310 includesmirrors 369A, 369B, and 369C, half wave plate 362, beam splitter 368,retroreflector 370 and an afocal system 365. A spatial filter 350 isplaced between polarizing beam splitter 320 and beam splitter 368.Interferometer 310 and measurement object 360 are separated by adistance L₄.

During operation, polarizing beam splitter 320 reflects a firstcomponent of an input beam 314 towards reference mirror 328, whiletransmitting a second orthogonal component which reflects frommeasurement object 360. Both components are reflected back towardspolarizing beam splitter 320. Quarter waveplates 322 and 324respectively cause the polarization state of each component to berotated through 90°, so that polarizing beam splitter 320 now transmitsthe first component but reflects the second component. Mirrors 369A,369B, and 369C relay both components back towards polarizing beamsplitter 320. Before the component beams contact the polarizing beamsplitter again, half wave plate 362 rotates the component beamspolarization through 90°, so that the polarizing beam splitter directsthe first component to reflect from measurement object 360 whiletransmitting the second component beam towards reference mirror 328. Thereflected component beams are then combined at polarizing beam splitter320 and exit the interferometer as output beam 316. Non-polarizing beamsplitter 368 directs a first portion of output beam 316 towards detector340. Detector 340 includes an analyzer, which samples a linearpolarization state of output beam 316. Detector 340 monitors theintensity of the sample polarization state.

Thus, both the first and second beams contact the measurement objectonce, at difference locations. These locations are separated by a knownamount, b₄. The phase of the detected intensity signal is related to thepath length difference between the first and second beams, which isrelated to the orientation of the measurement object.

A second portion of the output beam is transmitted by beam splitter 368and the second portion is subsequently reflected by retroreflector. 370and then transmitted by an afocal system 365 as a second input beam forinterferometer 310. The afocal system has a magnification of 2:1. Hence,any angular deviation (α) introduced in the output beam from the angulardisplacement interferometer caused by non-normal reflection from themeasurement object will be reduced to α/2. The resulting angulardeviation ensures that the directions of propagation of the measurementbeams of the interferometer at plane mirror measurement object 360 areorthogonal to the surface of the plane mirror measurement object.Examples of afocal systems are described below.

Interferometer 310 splits the second input beam into a measurement beamand a reference beam. The interferometer directs the measurement beam toreflect from measurement object 360 twice, and directs the referencebeam to reflect from reference mirror 328 twice before combining themeasurement and reference beams to form output beam 1320. A detector1340 monitors the intensity of a sampled polarization state of outputbeam 1320. The phase of the detected intensity signal is related to thedisplacement of measurement object 360 with respect to interferometer310.

An example of a Galilean afocal lens is shown diagrammatically in FIG.5(b) and a prismatic and birefringent anamorphic afocal attachments areshown diagrammatically in FIGS. 5(c) and 5(d), respectively. TheGalilean afocal lens shown in FIG. 5(b) include positive and negativelenses 177A and 177B, respectively, and illustrates its operation in ademagnifying mode.

A prismatic anamorphic afocal attachment, shown in FIG. 5(c), includestwo prisms 178A and 178B and also illustrates its operation in ademagnifying mode.

A birefringent anamorphic afocal attachment, shown in FIG. 5(d),includes two birefringent prisms 179A and 179C bonded together andillustrates its operation in a magnifying mode. The birefringent prismsmay include, for example, uniaxial crystals such as calcite andparatellurite. The optic axes for birefringent prisms 179A and 179C areshown in FIG. 5(d) as elements 179B and 179D, respectively. Polarizationof the input beam is extraordinary. The path of the input beam throughthe birefringent anamorphic afocal attachment and the directions for theoptic axes 179B and 179D are shown for a system comprising positiveuniaxial crystals wherein the ordinary index of refraction is less thanthe extraordinary index of refraction.

To illustrate the effect of spatial filter 150 on beam shear, assumethat the first and second component beams have Gaussian profiles, andthe spatial filter has a Gaussian transmission profile. AmplitudesA_(4,r,T) (ξ,η) and A_(4,m,T) (ξ,η) of the first and second componentbeams, respectively, of beam 320 are $\begin{matrix}{{A_{4,r,T}\left( {\xi,\eta} \right)} = {{T^{1/2}\left( {\xi,\eta} \right)}\quad{A_{4,r}\left( {\xi,\eta} \right)}}} & (53) \\{\quad{{= {A_{0}\quad\exp\begin{Bmatrix}\begin{matrix}{{{- \left\lbrack {\xi - {\left( \frac{u_{B,F}^{2}}{u_{B}^{2}} \right)\quad b_{4,\xi}}} \right\rbrack^{2}}\left( \frac{1}{u_{B,F}} \right)^{2}} -} \\{\left( \frac{u_{B,F}}{u_{F}} \right)^{2}\left( \frac{b_{4,\xi}}{u_{B}} \right)^{2}}\end{matrix} \\\begin{matrix}{{{- \left\lbrack {\eta - {\left( \frac{v_{B,F}^{2}}{v_{B}^{2}} \right)b_{4,\eta}}} \right\rbrack^{2}}\left( \frac{1}{v_{B,F}} \right)^{2}} -} \\{{\left( \frac{v_{B,F}}{v_{F}} \right)^{2}\left( \frac{b_{4,\eta}}{v_{B}} \right)^{2}} + {{\mathbb{i}}\quad\frac{\varphi_{4}}{2}}}\end{matrix}\end{Bmatrix}}},}} & \quad \\{{A_{4,m,T}\left( {\xi,\eta} \right)} = {{T^{1/2}\left( {\xi,\eta} \right)}\quad{A_{4,m}\left( {\xi,\eta} \right)}}} & (54) \\{\quad{= {A_{0}\quad\exp{\begin{Bmatrix}\begin{matrix}{{{- \left\lbrack {\xi - {\left( \frac{u_{B,F}^{2}}{u_{B}^{2}} \right)\quad b_{4,\xi}}} \right\rbrack^{2}}\left( \frac{1}{u_{B,F}} \right)^{2}} -} \\{\left( \frac{u_{B,F}}{u_{F}} \right)^{2}\left( \frac{b_{4,\xi}}{u_{B}} \right)^{2}}\end{matrix} \\\begin{matrix}{{{- \left\lbrack {\eta - {\left( \frac{v_{B,F}^{2}}{v_{B}^{2}} \right)b_{4,\eta}}} \right\rbrack^{2}}\left( \frac{1}{v_{B,F}} \right)^{2}} -} \\{{\left( \frac{v_{B,F}}{v_{F}} \right)^{2}\left( \frac{b_{4,\eta}}{v_{B}} \right)^{2}} + {{\mathbb{i}}\quad\frac{\varphi_{4}}{2}}}\end{matrix}\end{Bmatrix}.}}}} & \quad\end{matrix}$where A_(4,r) (ξ,η) and A_(4,m) (ξ,η) are the profiles of the first andsecond beams of beam 316.

Beam shears b_(4,ξ) and b_(4,η) that would be exhibited at detector 340if spatial filter 350 were removed and areb_(4,ξ)=2L₄θ_(4,ξ),  (55)b_(4,η)=2L₄θ_(4,η),  (56)where θ_(4,ξ) and θ_(4,η) are changes in orientation of plane mirror 360in the plane and orthogonal to the plane, respectively, of FIG. 4.

It is evident from Equations (53) and (54) that beam shears b_(4,ξ,T)and b_(4,η,T) of components of beam 320 are reduced relative tocorresponding beam shears of beam 316 according to the formulae$\begin{matrix}{{b_{4,\xi,T} = {\frac{u_{B,F}^{2}}{u_{B}^{2}}b_{4,\xi}}},} & (57) \\{{b_{4,\eta,T} = {\frac{v_{B,F}^{2}}{v_{B}^{2}}b_{4,\eta}}},} & (58)\end{matrix}$

A corresponding reduction of beam shears is also exhibited forcomponents of beam 1320.

The amplitude A_(4,H) of electrical interference signal 342 is obtainedby integrating the product of amplitudes A_(4,r,T) and A_(4,m,T) overthe ξ and η coordinates wherein the amplitudes are given by Equations(53) and (54). The resulting expression for A_(4,H) is $\begin{matrix}\begin{matrix}{A_{4,H} = {{A_{4,H,0}\left( \frac{\sqrt{2}u_{{2B},{2F}}}{u_{B}} \right)}\left( \frac{\sqrt{2}v_{{2B},{2F}}}{v_{B}} \right) \times}} \\{\exp\left\lbrack {{{- 4}\left( \frac{u_{{2B},{2F}}}{u_{F}} \right)^{2}\left( \frac{b_{4,\xi}}{u_{B}} \right)^{2}} - {4\left( \frac{v_{{2B},{2F}}}{v_{F}} \right)^{2}\left( \frac{b_{4,\eta}}{v_{B}} \right)^{2}}} \right\rbrack}\end{matrix} & (59)\end{matrix}$

where A_(4,H,0) is amplitude electrical interference signal 342 for thecase u_(F)=v_(F)=∞. The effects of φ₄ on amplitude A_(4,H) have been setto zero in obtaining Equation (59) to show in a simple example basicproperties of the invention without departing from the scope and spiritof the invention.

The value for the reduction of beam shear of the measurement beam ofbeam 320 and the amplitude ratio A_(4,H)/A^(4,H,0) for the case ofu_(F)=u_(F), v_(F)=∞ using Equations (57), (58), and (59) are$\begin{matrix}{{b_{4,\xi,T} = {\left( \frac{1}{2} \right)b_{4,\xi}}},} & (60) \\{{b_{4,\eta,T} = b_{4,\eta}},} & (61) \\{\left( \frac{A_{4,H}}{A_{4,H,0}} \right) = {\left( \frac{1}{2} \right)^{1/2}\quad{{\exp\left\lbrack {- \left( \frac{b_{\xi}}{u_{B}} \right)^{2}} \right\rbrack}.}}} & (62)\end{matrix}$

The values for the reduction of beam shear of the measurement beam ofbeam 320 and the amplitude ratio A_(4,H)/A_(4,H,0) for the case ofu_(B)=u_(F)=v_(B)=v_(F) using Equations (57), (58), and (59) are$\begin{matrix}{{b_{4,\xi,T} = {\left( \frac{1}{2} \right)b_{4,\xi}}},} & (63) \\{{b_{4,\eta,T} = {\left( \frac{1}{2} \right)b_{4,\eta}}},} & (64) \\{\left( \frac{A_{4,H}}{A_{4,H,0}} \right) = {\left( \frac{1}{2} \right)\quad{{\exp\left\lbrack {{- \left( \frac{b_{\xi}}{u_{B}} \right)^{2}} - \left( \frac{b_{\eta}}{v_{B}} \right)^{2}} \right\rbrack}.}}} & (65)\end{matrix}$

Note that the (b_(4ξ)/u_(B))² and (b_(4η)/u_(B))² in the exponent ofequations for A_(4,H)/A_(4,H,0) is generally a smaller term by a factorof 4 compared to the corresponding terms encountered in the first,second, and third embodiments (compare Equations (55) and (56) toEquations (7) and (8), Equations (25) and (26), and Equations (42) and(43).

Other examples of interferometry systems for measuring more than onedegree of freedom and for reducing beam shear are described in U.S.patent application Ser. No. 10/352,616 filed Jan. 28, 2003 and entitled“MULTIPLE-PASS INTERFEROMETRY” by Henry A. Hill. Other forms of multiplepass interferometers such as described in an article entitled“Differential interferometer arrangements for distance and anglemeasurements: Principles, advantages and applications” by C. Zanoni, VDIBerichte Nr. 749, 93-106 (1989) may also be characterized using system100 and/or 300.

Although the foregoing embodiments are with reference to HSPMI's, ingeneral, spatial filters can be used to reduce the effects of beam shearin other types of interferometer, such as single pass interferometers.Moreover, spatial filters can be used with interferometers that caninclude additional components to condition, redirect, or otherwisemanipulate the input beam, output beam, or measurement beam. An exampleof interferometers that includes such additional component(s) aredynamic interferometers. Examples of dynamic interferometers aredescribed in U.S. patent application Ser. No. 10/226,591 filed Aug. 23,2002 and entitled “DYNAMIC INTERFEROMETER CONTROLLING DIRECTION OF INPUTBEAM” by Henry A. Hill. Typically, a dynamic interferometer includes acomponent called a beam steering element. A beam steering element is anelement capable of changing the propagation direction a beam, usually inresponse to a signal based on the direction of the beam it is steering.An example of a beam steering element is a mirror coupled to atransducer that changes the orientation of the mirror based on a controlsignal. In dynamic interferometers, beam steering elements function tomaintain the orientation of the measurement beam substantiallyorthogonal to a plane mirror measurement object by adjusting thedirection of the measurement beam in response to changes in theorientation of the measurement object. The beam steering element may dothis by contacting the input beam or measurement beam. In someembodiments, the beam steering element contacts the output beam as well.

Spatial filters can also be used to reduce the effect of beam shear indispersion interferometers (e.g., two-wavelength dispersioninterferometers). Examples of two-wavelength dispersion interferometersare described in U.S. Pat. No. 6,219,144 B1 entitled “APPARATUS ANDMETHOD FOR MEASURING THE REFRACTIVE INDEX AND OPTICAL PATH LENGTHEFFECTS OF AIR USING MULTIPLE-PASS INTERFEROMETRY” by Henry A. Hill,Peter de Groot, and Frank C. Demarest and U.S. Pat. No. 6,327,039 B1 byPeter de Groot, Henry A. Hill, and Frank C. Demarest.

In some embodiments, the interferometer output beam is transported to aremotely located detector using a fiber optic pickup (FOP). Spatialfilters can be used to reduce beam shear of one or more beams in theoutput beam prior to coupling the output beam into the FOP. Examples ofinterferometry systems that utilize FOP's are described, for example, inU.S. patent application Ser. No. 09/599,348, entitled “INTERFEROMETRYSYSTEM HAVING A DYNAMIC BEAM-STEERING ASSEMBLY FOR MEASURING ANGLE ANDDISTANCE AND EMPLOYING OPTICAL FIBERS FOR REMOTE PHOTOELECTRICDETECTION,” filed Jun. 20, 2000, by Henry A. Hill.

While the use of a spatial filter can reduce non-cyclic errors byreducing beam shear, other sources of error can also contribute touncertainty in interferometry measurements. For example, anotherpotential source of errors are time-varying effects of gas in the pathof the measurement beam. In some embodiments, in addition to using aspatial filter, interferometry systems can compensate for these errorsusing techniques described in U.S. patent application Ser. No.10/294,158 entitled “COMPENSATING FOR EFFECTS OF VARIATIONS IN GASREFRACTIVITY IN INTERFEROMETERS,” filed Nov. 14, 2002, U.S. patentapplication Ser. No. 10/309,394 entitled “COMPENSATING FOR EFFECTS OFNON-ISOTROPIC GAS MIXTURES IN INTERFEROMETERS,” filed on Dec. 3, 2002and U.S. patent application Ser. No. 10/350,522 entitled “METHOD ANDAPPARATUS FOR COMPENSATION OF TIME-VARYING OPTICAL PROPERTIES OF GAS ININTERFEROMETERY” filed Jan. 24, 2003, all by Henry A. Hill.

Non-cyclic errors can be further reduced by pre-characterizing errors inthe system using techniques disclosed in U.S. patent application Ser.No. 10/366,587, entitled “CHARACTERIZATION AND COMPENSATION OFNON-CYCLIC ERRORS IN INTERFEROMETRY SYSTEMS,” and U.S. patentapplication Ser. No. 10/366,676, entitled “METHOD AND APPARATUS TOMEASURE FIBER OPTIC PICKUP ERRORS IN INTERFEROMETRY SYSTEMS,” both filedFeb. 12, 2003, both by Henry A. Hill.

The observed phase can also be compensated for contributions from cyclicerrors. In order to compensate for these contributions, a cyclic errorcompensating system can be used to determine a cyclic error functioncharacterizing the cyclic error contribution to the observed phase forthe interferometer. Examples of cyclic error compensating systems aredescribed in U.S. patent application Ser. No. 10/287,898 entitled“INTERFEROMETRIC CYCLIC ERROR COMPENSATION” filed Nov. 5, 2002 by HenryA. Hill, and U.S. patent application Ser. No. 10/174,149 and entitled“INTERFEROMETRY SYSTEM AND METHOD EMPLOYING AN ANGULAR DIFFERENCE INPROPAGATION BETWEEN ORTHOGONALLY POLARIZED INPUT BEAM COMPONENTS” filedJun. 17, 2002 by Peter de Groot and Henry A. Hill.

The interferometry systems described above provide highly accuratemeasurements. Such systems can be especially useful in lithographyapplications used in fabricating large scale integrated circuits such ascomputer chips and the like. Lithography is the key technology driverfor the semiconductor manufacturing industry. Overlay improvement is oneof the five most difficult challenges down to and below 100 nm linewidths (design rules), see for example the Semiconductor IndustryRoadmap, p82 (1997).

Overlay depends directly on the performance, i.e. accuracy andprecision, of the distance measuring interferometers used to positionthe wafer and reticle (or mask) stages. Since a lithography tool mayproduce $50-100 M/year of product, the economic value from improvedperformance distance measuring interferometers is substantial. Each 1%increase in yield of the lithography tool results in approximately $1M/year economic benefit to the integrated circuit manufacturer andsubstantial competitive advantage to the lithography tool vendor.

The function of a lithography tool is to direct spatially patternedradiation onto a photoresist-coated wafer. The process involvesdetermining which location of the wafer is to receive the radiation(alignment) and applying the radiation to the photoresist at thatlocation (exposure).

To properly position the wafer, the wafer includes alignment marks onthe wafer that can be measured by dedicated sensors. The measuredpositions of the alignment marks define the location of the wafer withinthe tool. This information, along with a specification of the desiredpatterning of the wafer surface, guides the alignment of the waferrelative to the spatially patterned radiation. Based on suchinformation, a translatable stage supporting the photoresist-coatedwafer moves the wafer such that the radiation will expose the correctlocation of the wafer.

During exposure, a radiation source illuminates a patterned reticle,which scatters the radiation to produce the spatially patternedradiation. The reticle is also referred to as a mask, and these termsare used interchangeably below. In the case of reduction lithography, areduction lens collects the scattered radiation and forms a reducedimage of the reticle pattern. Alternatively, in the case of proximityprinting, the scattered radiation propagates a small distance (typicallyon the order of microns) before contacting the wafer to produce a 1:1image of the reticle pattern. The radiation initiates photo-chemicalprocesses in the resist that convert the radiation pattern into a latentimage within the resist.

Interferometry systems are important components of the positioningmechanisms that control the position of the wafer and reticle, andregister the reticle image on the wafer. If such interferometry systemsinclude the features described above, the accuracy of distances measuredby the systems increases as error contributions to the distancemeasurement are minimized.

In general, the lithography system, also referred to as an exposuresystem, typically includes an illumination system and a waferpositioning system. The illumination system includes a radiation sourcefor providing radiation such as ultraviolet, visible, x-ray, electron,or ion radiation, and a reticle or mask for imparting the pattern to theradiation, thereby generating the spatially patterned radiation. Inaddition, for the case of reduction lithography, the illumination systemcan include a lens assembly for imaging the spatially patternedradiation onto the wafer. The imaged radiation exposes resist coatedonto the wafer. The illumination system also includes a mask stage forsupporting the mask and a positioning system for adjusting the positionof the mask stage relative to the radiation directed through the mask.The wafer positioning system includes a wafer stage for supporting thewafer and a positioning system for adjusting the position of the waferstage relative to the imaged radiation. Fabrication of integratedcircuits can include multiple exposing steps. For a general reference onlithography, see, for example, J. R. Sheats and B. W. Smith, inMicrolithoraphy: Science and Technology (Marcel Dekker, Inc., New York,1998), the contents of which is incorporated herein by reference.

Interferometry systems described above can be used to precisely measurethe positions of each of the wafer stage and mask stage relative toother components of the exposure system, such as the lens assembly,radiation source, or support structure. In such cases, theinterferometry system can be attached to a stationary structure and themeasurement object attached to a movable element such as one of the maskand wafer stages. Alternatively, the situation can be reversed, with theinterferometry system attached to a movable object and the measurementobject attached to a stationary object.

More generally, such interferometry systems can be used to measure theposition of any one component of the exposure system relative to anyother component of the exposure system, in which the interferometrysystem is attached to, or supported by, one of the components and themeasurement object is attached, or is supported by the other of thecomponents.

An example of a lithography scanner 1100 using an interferometry system1126 is shown in FIG. 5 a. The interferometry system is used toprecisely measure the position of a wafer (not shown) within an exposuresystem. Here, stage 1122 is used to position and support the waferrelative to an exposure station. Scanner 1100 includes a frame 1102,which carries other support structures and various components carried onthose structures. An exposure base 1104 has mounted on top of it a lenshousing 1106 atop of which is mounted a reticle or mask stage 1116,which is used to support a reticle or mask. A positioning system forpositioning the mask relative to the exposure station is indicatedschematically by element 1117. Positioning system 1117 can include,e.g., piezoelectric transducer elements and corresponding controlelectronics. Although, it is not included in this described embodiment,one or more of the interferometry systems described above can also beused to precisely measure the position of the mask stage as well asother moveable elements whose position must be accurately monitored inprocesses for fabricating lithographic structures (see supra Sheats andSmith Microlithography: Science and Technology).

Suspended below exposure base 1104 is a support base 1113 that carrieswafer stage 1122. Stage 1122 includes a plane mirror 1128 for reflectinga measurement beam 1154 directed to the stage by interferometry system1126. A positioning system for positioning stage 1122 relative tointerferometry system 1126 is indicated schematically by element 1119.Positioning system 1119 can include, e.g., piezoelectric transducerelements and corresponding control electronics. The measurement beamreflects back to the interferdmetry system, which is mounted on exposurebase 1104. The interferometry system can be any of the embodimentsdescribed previously.

During operation, a radiation beam 1110, e.g., an ultraviolet (UV) beamfrom a UV laser (not shown), passes through a beam shaping opticsassembly 1112 and travels downward after reflecting from mirror 1114.Thereafter, the radiation beam passes through a mask (not shown) carriedby mask stage 1116. The mask (not shown) is imaged onto a wafer (notshown) on wafer stage 1122 via a lens assembly 1108 carried in a lenshousing 1106. Base 1104 and the various components supported by it areisolated from environmental vibrations by a damping system depicted byspring 1120.

In other embodiments of the lithographic scanner, one or more of theinterferometry systems described previously can be used to measuredistance along multiple axes and angles associated for example with, butnot limited to, the wafer and reticle (or mask) stages. Also, ratherthan a UV laser beam, other beams can be used to expose the waferincluding, e.g., x-ray beams, electron beams, ion beams, and visibleoptical beams.

In some embodiments, the lithographic scanner can include what is knownin the art as a column reference. In such embodiments, theinterferometry system 1126 directs the reference beam (not shown) alongan external reference path that contacts a reference mirror (not shown)mounted on some structure that directs the radiation beam, e.g., lenshousing 1106. The reference mirror reflects the reference beam back tothe interferometry system. The interference signal produce byinterferometry system 1126 when combining measurement beam 1154reflected from stage 1122 and the reference beam reflected from areference mirror mounted on the lens housing 1106 indicates changes inthe position of the stage relative to the radiation beam. Furthermore,in other embodiments the interferometry system 1126 can be positioned tomeasure changes in the position of reticle (or mask) stage 1116 or othermovable components of the scanner system. Finally, the interferometrysystems can be used in a similar fashion with lithography systemsinvolving steppers, in addition to, or rather than, scanners.

As is well known in the art, lithography is a critical part ofmanufacturing methods for making semiconducting devices. For example,U.S. Pat. No. 5,483,343 outlines steps for such manufacturing methods.These steps are described below with reference to FIGS. 5 b and 5 c.FIG. 5 b is a flow chart of the sequence of manufacturing asemiconductor device such as a semiconductor chip (e.g. IC or LSI), aliquid crystal panel or a CCD. Step 1151 is a design process fordesigning the circuit of a semiconductor device. Step 1152 is a processfor manufacturing a mask on the basis of the circuit pattern design.Step 1153 is a process for manufacturing a wafer by using a materialsuch as silicon.

Step 1154 is a wafer process which is called a pre-process wherein, byusing the so prepared mask and wafer, circuits are formed on the waferthrough lithography. To form circuits on the wafer that correspond withsufficient spatial resolution those patterns on the mask,interferometric positioning of the lithography tool relative the waferis necessary. The interferometry methods and systems described hereincan be especially useful to improve the effectiveness of the lithographyused in the wafer process.

Step 1155 is an assembling step, which is called a post-process whereinthe wafer processed by step 1154 is formed into semiconductor chips.This step includes assembling (dicing and bonding) and packaging (chipsealing). Step 1156 is an inspection step wherein operability check,durability check and so on of the semiconductor devices produced by step1155 are carried out. With these processes, semiconductor devices arefinished and they are shipped (step 1157).

FIG. 5 c is a flow chart showing details of the wafer process. Step 1161is an oxidation process for oxidizing the surface of a wafer. Step 1162is a CVD process for forming an insulating film on the wafer surface.Step 1163 is an electrode forming process for forming electrodes on thewafer by vapor deposition. Step 1164 is an ion implanting process forimplanting ions to the wafer. Step 1165 is a resist process for applyinga resist (photosensitive material) to the wafer. Step 1166 is anexposure process for printing, by exposure (i.e., lithography), thecircuit pattern of the mask on the wafer through the exposure apparatusdescribed above. Once again, as described above, the use of theinterferometry systems and methods described herein improve the accuracyand resolution of such lithography steps.

Step 1167 is a developing process for developing the exposed wafer. Step1168 is an etching process for removing portions other than thedeveloped resist image. Step 1169 is a resist separation process forseparating the resist material remaining on the wafer after beingsubjected to the etching process. By repeating these processes, circuitpatterns are formed and superimposed on the wafer.

The interferometry systems described above can also be used in otherapplications in which the relative position of an object needs to bemeasured precisely. For example, in applications in which a write beamsuch as a laser, x-ray, ion, or electron beam, marks a pattern onto asubstrate as either the substrate or beam moves, the interferometrysystems can be used to measure the relative movement between thesubstrate and write beam.

As an example, a schematic of a beam writing system 1200 is shown inFIG. 6. A source 1210 generates a write beam 1212, and a beam focusingassembly 1214 directs the radiation beam to a substrate 1216 supportedby a movable stage 1218. To determine the relative position of thestage, an interferometry system. 1220 directs a reference beam 1222 to amirror 1224 mounted on beam focusing assembly 1214 and a measurementbeam 1226 to a mirror 1228 mounted on stage 1218. Since the referencebeam contacts a mirror mounted on the beam focusing assembly, the beamwriting system is an example of a system that uses a column reference.Interferometry system 1220 can be any of the interferometry systemsdescribed previously. Changes in the position measured by theinterferometry system correspond to changes in the relative position ofwrite beam 1212 on substrate 1216. Interferometry system 1220 sends ameasurement signal 1232 to controller 1230 that is indicative of therelative position of write beam 1212 on substrate 1216. Controller 1230sends an output signal 1234 to a base 1236 that supports and positionsstage 1218. In addition, controller 1230 sends a signal 1238 to source1210 to vary the intensity of, or block, write beam 1212 so that thewrite beam contacts the substrate with an intensity sufficient to causephotophysical or photochemical change only at selected positions of thesubstrate.

Furthermore, in some embodiments, controller 1230 can cause beamfocusing assembly 1214 to scan the write beam over a region of thesubstrate, e.g., using signal 1244. As a result, controller 1230 directsthe other components of the system to pattern the substrate. Thepatterning is typically based on an electronic design pattern stored inthe controller. In some applications the write beam patterns a resistcoated on the substrate and in other applications the write beamdirectly patterns, e.g., etches, the substrate.

An important application of such a system is the fabrication of masksand reticles used in the lithography methods described previously. Forexample, to fabricate a lithography mask an electron beam can be used topattern a chromium-coated glass substrate. In such cases where the writebeam is an electron beam, the beam writing system encloses the electronbeam path in a vacuum. Also, in cases where the write beam is, e.g., anelectron or ion beam, the beam focusing assembly includes electric fieldgenerators such as quadrapole lenses for focusing and directing thecharged particles onto the substrate under vacuum. In other cases wherethe write beam is a radiation beam, e.g., x-ray, UV, or visibleradiation, the beam focusing assembly includes corresponding optics andfor focusing and directing the radiation to the substrate.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention. Forexample, although the foregoing embodiment of a spatial filter includespair of lenses and a pinhole aperture, other components can be used. Thespatial filter can include one or more additional or alternative opticalcomponents (e.g., diffractive, refractive, and/or holographiccomponent(s)) to reduce deviations of the measurement beam from thenominal measurement beam path. Accordingly, other aspects, advantages,and modifications are within the scope of the following claims.

1. A method, comprising: directing a first beam and a second beam along respective paths, wherein the first beam contacts a measurement object and changes in the orientation of the measurement object cause a displacement of the first beam from a nominal beam path, and wherein the first and second beams are derived from a common source; spatial filtering the first beam after it contacts the measurement object, wherein the spatial filtering reduces the displacement of the first beam from the optical path; and combining the first and second beams to form an output beam, wherein the output beam comprises information about an optical path length difference between the first and second beams, wherein the first beam is spatially filtered prior to being combined with the second beam.
 2. The method of claim 1, wherein the displacement of the first beam from the nominal beam path causes a measurable interferometric phase, Φ, derived from the output beam to deviate from the expression Φ=pknL, where p is an integer, k is the wavenumber of the output beam, and nL corresponds to the optical path length difference.
 3. The method of claim 2, wherein the deviation of Φ from the expression Φ=pknL comprises a non-cyclic error term that varies in a nonperiodic way on the optical path length difference.
 4. The method of claim 1, wherein the nominal path corresponds to the first beam path when the measurement object is in a reference orientation.
 5. The method of claim 4, wherein the first beam is normally incident on the measurement object when the measurement object is in the reference orientation.
 6. A method, comprising: directing a first beam and a second beam along respective paths using a high stability plane mirror interferometer, wherein the first beam contacts a measurement object and wherein the first and second beams are derived from a common source; spatial filtering the first beam after it contacts the measurement object; and combining the first and second beams to form an output beam, wherein the output beam comprises information about an optical path length difference between the first and second beams.
 7. The method of claim 6, wherein changes in the orientation of the measurement object cause a displacement of the first beam from a nominal beam path.
 8. The method of claim 7, wherein the spatial filtering reduces the displacement of the first beam from the nominal beam path.
 9. The method of claim 7, wherein the nominal path corresponds to the first beam path when the measurement object is in a reference oriented.
 10. The method of claim 7, wherein the displacement of the first beam from the nominal beam path causes a measurable interferometric phase, Φ, derived from the output beam to deviate from the expression Φ=pknL, where p is an integer, k is the wavenumber of the output beam, and nL corresponds to the optical path length difference.
 11. The method of claim 10, wherein the deviation of Φ from the expression Φ=pknL comprises a non-cyclic error term that varies in a nonperiodic way on the optical path length difference.
 12. A method, comprising: directing a first beam and a second beam along respective paths, wherein the first beam contacts a measurement object more than once and wherein the first and second beams are derived from a common source; spatial filtering the first beam after it contacts the measurement object; and combining the first and second beams to form an output beam, wherein the output beam comprises information about an optical path length difference between the first and second beams.
 13. The method of claim 12, wherein the first beam contacts the measurement object twice.
 14. The method of claim 12, wherein changes in the orientation of the measurement object cause a displacement of the first beam from a nominal beam path.
 15. The method wherein the spatial filtering reduces the displacement of the first beam from the nominal beam path.
 16. The method of claim 14, wherein the nominal path corresponds to the first beam path when the measurement object is in a reference oriented.
 17. A method, comprising: directing a first beam and a second beam along respective paths, wherein the first beam contacts a measurement object and wherein the first and second beams are derive from a common source; spatial filtering the first beam after it contacts the measurement object; and combining the first and second beams to form an output beam, wherein the output beam comprises information about an optical path length difference between the first and second beams, wherein the first beam is spatially filtered prior to being combined with the second beam.
 18. The method of claim 17, wherein changes in the orientation of the measurement object cause a displacement of the first beam from a nominal beam path.
 19. The method of claims 18, wherein the spatial filtering reduces the displacement of the first beam from the nominal beam path.
 20. The method of claim 18, wherein the nominal path corresponds to the first beam path when the measurement object is in a reference oriented.
 21. An apparatus, comprising: an interferometer which during operation directs a first beam and a second beam along respective paths and then combines the first and second beams to produce an output beam, wherein the first beam contacts a measurement object more than once and changes in the orientation of the measurement object cause a displacement of the first beam from a nominal beam path, and wherein the output beam comprises information about an optical path length difference between the first and second beams; and a spatial filter positioned in the path of the first beam, wherein the spatial filtering reduces the displacement of the first beam from the nominal beam path.
 22. The apparatus of claim 21, wherein the interferometer directs the first beam to contact the measurement object twice.
 23. The apparatus of claim 22, wherein the interferometer is a high stability plane mirror interferometer.
 24. An apparatus, comprising: a high stability plane mirror interferometer which during operation directs a first beam and a second beam along respective paths and then combines the first and second beams to produce an output beam, wherein the first beam contacts a measurement object and changes in the orientation of the measurement object cause a displacement of the first beam a nominal beam path, and wherein the output beam comprises information about an optical path length difference between the first and second beams; and a spatial filter positioned in the path of the first beam, wherein the spatial filtering reduces the displacement of the first beam from the nominal beam path. 